Telkes, daughter of Aladar Telkes and Maria Laban de Telkes, was raised in Budapest. She studied physical chemistry at the University of Budapest, graduating with a B.A. in 1920 and a Ph.D. in 1924. She became an instructor at the institution in 1924 but decided to immigrate to the United States after visiting a relative, who served at the time as the Hungarian consul in Cleveland. In 1925 she accepted a position as a biophysicist for the Cleveland Clinic Foundation, where she worked with American surgeon George Washington Crile to create a photoelectric device that recorded brain waves.
Telkes became an American citizen in 1937. That same year she became a research engineer at Westinghouse Electric, where she developed instruments that converted heat into electrical energy; however, she made her first forays into solar energy research in 1939. That year, as part of the Solar Energy Conversion Project at the Massachusetts Institute of Technology (MIT), she worked on thermoelectric devices powered by sunlight. Telkes was assigned to the U.S. Office of Scientific Research and Development during World War II, and it was there that she created one of her most important inventions: a solar distiller capable of vaporizing seawater and recondensing it into drinkable water. Although the system was carried aboard life rafts during the war, it was also scaled up to supplement the water demands of the Virgin Islands. She remained at MIT after the war, becoming an associate research professor in metallurgy in 1945.